Question 170677
Find a five digit number in which the second and fourth digits are the same,
ABCBE
:
 the third digit is the sum of the first and second,
C = A+B
:
the fifth digit is the sum of the third and fourth
E = C + B
:
the third digit is one more than the first
C = A + 1
A = C - 1
:
Also the third digit is one less than the fifth.
C = E - 1
E = C + 1
;
 The sum of all the digits is 14.
A + B + C + B + E = 14
A + 2B + C + E = 14
:
Looking at our equations we see:
E = C + B
And
E = C + 1
Therefore
B = 1
:
Substituting 1 for B in the Sum equation
A + 2(1) + C + E = 14
A + C + E = 14 - 2
A + C + E = 12
:
Substitute (C-1) for A, and (C+1) for E, find C
(C-1) + C + (C+1) = 12
3C = 12
C = 4
Then
A = 4 - 1
A = 3
and
E = 4 + 1
E = 5
:
Our number is: 31415
:
:
Check solution:
 the third digit is the sum of the first and second,
4 = 3 + 1
:
 the fifth digit is the sum of the third and fourth
5 = 4 + 1
:
and the third digit is one more than the first and one less than the fifth.
4 = 3 + 1
:
 The sum of all the digits is 14.
3 + 1 + 4 + 1 + 5 = 14